A Space of Apt Product Designs Based on Market Information

Featured Application

Applications can be found in industries, services, and other areas of human activity where products are designed to be brought out to the market. The proposed methodology requires information technologies because the methods are data-driven.

Abstract

This paper describes procedures that can be adopted during product development, so that there is a higher chance that new products are properly designed before being placed on the market. To implement the suggested procedures, market data are first obtained, then processed in a specified way for the new products to reflect relevant market information. This means putting into use suitable data-processing algorithms and information technologies, based on the type of collected information. The text deals with two information scenarios in this regard, the first assuming that not much is known about customers’ desires and the second working with larger amounts of more specific customer data. While the former requires a more sophisticated approach to product design, theoretically speaking, the latter is simpler to handle from the theoretical point of view, but potentially less so from a practical perspective, given the amounts of data. These theoretical and practical problems are discussed in what follows, and their possible solutions are presented.

1. Introduction

It is certainly of great interest to companies to identify product characteristics in their own market that appeal to the market, as well as their desired levels. Only then can they succeed in the increasingly competitive corporate world. To obtain such valuable knowledge about the features and levels, companies should monitor the market and get as much information about its behavior as possible, in addition to realizing the technical limits which determine their own production capabilities. If some market information is available, the question is how to process it, as product design-appropriate procedures will generally depend on the type of information acquired. When more market data is available, the overall situation seems rather promising for a good product design to be developed, based on the data, although lots of data—something the business sphere is capable of generating these days—may bring some problems, as well, the main trouble being not so much the data processing time as the processing techniques themselves. When, on the contrary, there is little consumer information available, the problem of whether there is any chance at all to design a suitable product arises.

The presented text deals with the two data situations just outlined and suggests data-driven procedures that can help companies realize whether the product they have been offering to the market makes enough sense, or, if they have not done so, what kind of product they should start manufacturing. Regarding the scenario when enough market data is available, this paper presents analytical steps and their automated software implementation that can lead to a set of potentially appropriate product designs. The steps can be applied directly in practice when determining such designs. Apart from the procedural concept, which is simple, the text points out some of the pitfalls likely to be encountered when not enough attention is paid to the implementation of software-based automation, especially in the presence of larger amounts of data. As far as the adverse data scenario is concerned, the paper describes a procedure that identifies a product space within which the company can operate when looking for an appropriate product design, as unfortuitous as the situation may seem at first. To detect the product space, the theory of multicriteria decision making is applied in this less fortunate case.

The first scenario analyzed in the text is the less favorable one, when little market information is available, since this is the situation that can be fairly frequently encountered in practice. In the subsequent part of the text, the more favorable scenario is examined. Both situations and their suggested solutions are illustrated using specific numerical examples. Also, after the exposition of the procedures, which takes place in Section 2, and demonstrating them with examples in the Section 3, the adverse-scenario method is compared to other methods that have been historically known to try to solve similar problems in the Section 4.

2. Materials and Methods

Two situations shall be described and dealt with, one assuming that very little information about the market is available, the other providing, on the contrary, lots of market data which must be processed and automated correctly using suitable technologies.

Since not much is known about individual customers in the first scenario, it is necessary to take a model-based approach that will try to estimate customers’ behavioral habits. Once an estimate is available, product designs can subsequently be suggested that will draw on these habits. The models require some inputs as well, however, and in this text, the inputs are represented by the overall sales of the existing variants of an observed product, i.e., by information about the corresponding market as a whole. Accordingly, it is assumed for the model to be used that it is known which product variant has been the top seller, and if necessary, which variant ranked second in sales, third, etc. Further, it is assumed that it is known which product characteristics might generally be observed by customers for a given product and whether they are preferred to be minimized or maximized. Such general knowledge is usually available. As an example, it can certainly be said that when it comes to cars, for instance, customers observe engine power, maximal speed, and fuel consumption, among other things, and it is obvious whether higher levels of these features are perceived better or worse. On the other hand, it is much harder to recognize which of these characteristics are preferred more, to the detriment of others, and to what extent exactly for each individual customer. Thus, what is important in this information scenario is that more specific preferences of individual customers are outside companies’ knowledge, and rather general information about the entire market is available only.

If product characteristics are mutually independent, it is possible to use the Analytic Hierarchy Process (AHP) theory as a behavioral model [1], as is done in what follows. This would be the situation when customers are, for instance, so interested in technical features of a product that nothing else, including price, was of interest to them. In many instances, however, price will probably also be a considered feature, in which case a dependence will exist among the characteristics, since price is a function of other features. The case of dependent features is also commented on later in the text.

The AHP model is a procedure that helps a decision-maker solve a multicriteria decision-making problem; that is, it helps find among decision-making variants the one that could best fit his/her needs, and although no mathematical model can fully embrace one’s behavior, experience is such that decision-makers using the model often see in the outcome provided by the model a variant which is not far from the variant he or she would have intuitively selected had there been no model. Thus, the model can be applied to at least approximately identify the product variant among the considered variants that might be the most prioritized by the decision-maker; it will be the variant with the highest value assigned to it by the AHP model. The outcome returned by the model can be expected to be either the product variant that appeals the most, or at least a variant which is not far from the most appealing variant. The evaluation of an ith product variant by the AHP model is such that if the quantified level of its jth characteristic is $a_{ij}$ and the importance or weight of the jth characteristic is $w_j\in [0,1]$—usually determined by a method of pairwise comparisons [1,2]—the ith variant has an overall AHP-based value of ${\sum }_j{w}_j{\ddot{a}}_{ij}$, where ${\ddot{a}}_{ij}$ is the result of normalizing $a_{ij}$: ${\ddot{a}}_{ij}=a_{ij}/{\sum }_i{a}_{ij}$, if the jth feature is preferred to be maximized, or ${\ddot{a}}_{ij}=(1/a_{ij})/{\sum }_i(1/a_{ij})$, if the jth characteristic is preferred to be minimized. The index i is from the set of indices assigned to the analyzed product variants, the index j is from the set of indices reserved for the observed product characteristics. This concept can now be used in practice for the business objectives outlined earlier in the text as follows:

(1)

Using interval [0, 1] for each weight that represents importance of a product feature, find weight combinations $k_i$, $i=1,\dots ,n$, where $k_i$ is the ith vector of weights chosen from $[0,1]\times \dots \times [0,1]$, which have the property that when used in the AHP model, the currently top-selling product variant has the highest overall AHP-based value among the currently sold variants. Not all weight vectors from the multivariate interval will have this property. The weight vectors that lead to the best-selling product having the highest AHP value form a space potentially containing weight vectors used in the decision-making process by the clients who bought the best-selling variant, at least according to the AHP model. This is because, as described, the top seller can be expected to have the highest AHP value among the sold variants for those who bought it, or a value near the maximum.

In practice, the interval $[0,1]\times \dots \times [0,1]$, which contains an infinite number of weight vectors, should be reasonably discretized when finding the weights.

(2)

Within the technical capabilities of the company that seeks a good product design, generate new product variants $p_j$, $j=1,\dots ,m$, and calculate their AHP values $A_{ij}$, using the sets of weights $k_i$ from step 1.

(3)

For each generated product variant $p_j$, form the set $M_j$ of all those combinations of weights $k_i$ for which $A_{ij}$ is higher than the AHP value of all the currently sold product variants, or at least as high as the AHP value of the current top seller.

(4)

A suitable product variant is the variant $p_k$ whose set $M_k$ is the largest of all $M_j$ sets.

Step 1 works with the top-selling product variant, demanded by a potentially interesting number of clients, given that it is a top seller. Within the AHP approach, this variant should have the highest AHP value among all the variants currently sold, for those clients. Step 1 therefore finds various decision-making weights that lead to this expected result. The found weights encapsulate as an estimate the clients’ weights, or their preferences regarding the product features. The knowledge of the clients’ weights is important, for if they are known, a new variant, even more successful than the currently most successful variant, can be designed; the design should have such characteristics that, using the known weights, its AHP value will be higher than that of any existing variant. Such a product design could appeal to the market segment. But the weights are not known exactly and so step 1 creates a whole space of weights that is assumed to contain the unknown weights of the clients whose purchases gave rise to the top-selling product. In step 2, each newly generated product variant is evaluated with all the sets of weights obtained in step 1. This way, all these evaluations will contain, within the modelling, the “true” evaluations of the variant made by the clients from step 1. Now, since the desire is to create a variant potentially better than any of the existing variants, its AHP value should be the highest (step 3 of the procedure) and with respect to as many step 1 weights as possible (step 4 of the procedure) to increase the chance that it is indeed the best product variant for the discussed client segment, or at least its part. This is because it is unknown where exactly in the step 1 space of weights the clients’ true weights are located, so the intent is to cover as much of that space as possible to capture the clients, or as many of them as possible.

To run the procedure in practice, the R programming language, Python, or other similar means can be used, which allows the generation of the repeated actions contained in steps 1–3 of the procedure. In the example shown in Section 3, the R programming, version 2023.12.1+402, is used.

Regarding the second information scenario, a situation may occur when more information on customers’ preferences is known. This can happen, for instance, through internet forums run by a company’s representative or an outside contributor. The forums often run a poll to detect users’ preferences, and they are rather quietly observed by companies because it is a simple way for them to learn more about their customers in an unobtrusive way. When such information is available, it is fairly straightforward to develop a concept of exploiting it, so that a product can be designed that appeals to clients. What may not be as clear, however, is how to implement the concept when the information is available from a large number of clients, since some less obvious problems may occur along the way. Using a specific example, the concept and its implementation with proper information technologies will be described, reflecting on the potential pitfalls that may elude one’s attention in the process. The concept itself is rudimentary. The problem of creating a rational product design can be approached as follows under the current data scenario:

(1)

Taking into account preferences of the ith client, create a set $M_i$ of product configurations that fall within these preferences. Doing so for each client from the market sample, a set $M={\bigcup }_i{M}_i$ of potentially interesting product configurations is established. Each configuration contained in M addresses at least one client.

(2)

Find out which product configuration from $M$ satisfies the largest number of customers from the market sample. If a product variant is to satisfy a customer, its attributes must fall within the barriers defined by the customer’s preferences.

To implement the two steps in the presence of larger amounts of data, a couple tools are required: a programming environment to generate product configurations that can be manufactured and satisfy the needs of a given client (step 1 of the procedure), and a visualization tool that displays how many generated product configurations are shared (step 2 of the procedure). Visualization tools that best fit the needs given by step 2 belong to the category of business intelligence. Their advantage is relative simplicity with which they interact with data; their disadvantage is that, although they usually have their own programming language, the coding does not have the properties of a full-grown programming, which means that it does not provide a way to create repetitive actions, such as the programming-specific cycles needed to generate product configurations in step 1.

As straightforward as the concept and its implementation just described may seem, there are some pitfalls that can be unwillingly and easily overseen and should be avoided. Regarding the generation of product configurations in step 1, this will usually be done in such a way that for each product feature, its space of possible configurations will be run through in a computer system, but this procedure cannot be done automatically without noticing that relations may exist among product characteristics, as will often be the case. If there are indeed such dependencies, a fully automatic generation of product variants will most certainly result in having some variants that are impossible to produce. Such product configurations should not enter the analysis, of course, since they cannot be produced in the first place. To avoid the situation, product features should be divided into two categories: the independent and those that depend on them. Only the independent are then generated in their different combinations within a computer system, while the dependent are set up additionally, based on the form of their dependence on the independent features. To give an example, if a product has three features, the first two being technical and the third depending on the two proportionately, then the combination “feature one at its top level, feature two at its top level, and feature three at its bottom level” will be an impossible configuration despite being proposed by a computer system working with programmed cycles.

Further, it should be taken into account that some information pieces are likely to be duplicated or shared within the same client; for instance, there may be several product configurations in line with a client’s preferences, which are on the same level regarding a specific product feature. If the task is to count how many clients want this specific feature level, as commanded by step 2 of the procedure, the client in question should naturally be counted only once and not several times, as the number of product configurations suggests in this case. Thus, in a system analyzing data, duplication issues must be resolved.

Thirdly, if the largest number of clients obtained in step 2 is not large enough and so there is no “clear winner” among product configurations, it is possible to think about product features that are easy to alter at the end of the production and focus the analysis on a smaller number of features which must be determined before or during the production and are impossible to change after the production. This way, product designs with respect to a smaller number of more fundamental features can be analyzed in terms of how many customers they address. The advantage of this procedure is that, since fewer features are observed, the chance is higher that there will be more customers whose preferences are satisfied by a given configuration of the fewer features. To give an example, let a product bear three features P1, P2, P3, the first two of which are technically demanding, while the last is color, which can be easily altered once the first two features have been manufactured. If there were two customers with similar priorities regarding P1 and P2, then both of them can be satisfied within step 2, which will seek an intersection of their preferences only with respect to P1 and P2; the company can run a production of the one product configuration satisfying both clients with respect to P1 and P2, and in the end, add a suitable color to the product for each client. Both customers will be acquired. If a product configuration was sought with respect to all three features in an automated, less-attended system and clients’ opinion on color was different, only one client would lie in the intersection of all the preferences and only one would be acquired. Thus, regarding the number of product features analyzed, the IT implementation of the product analysis should enable the IT user to select with respect to which features the analysis of clients’ preferences should be carried out.

The two-step procedure is demonstrated in Section 3 with specific data. The implementation is carried out with the Tableau visualization tool in this case, which allows generation of product configurations and the finding of the intersections of clients’ needs with respect to those configurations, as described above. Other tools with similar functionality can be applied, as well.

3. Results

To see the effect of the outlined methodology, several examples will now be presented. First, the following general example visualizes the logic of the four-step procedure working with little market information. It deals with four product characteristics, hence four weights $w_j$. Figure 1 contains between lines A and B four true weights of client 1 (the vertical side of the box is thought of as a numeric axis quantifying weights in this basic visualization). The quadruplet between lines B and C represents the true weights of client 2, and between lines C and D, there are true weights of clients 3 and 4. The four clients, in this elementary example, represent the segment of the market that bought the top-selling product. The product is a top seller thanks to these four clients. The entire box is considered to be a symbolic visualization of the step 1 space of weights (most of them not shown in the graph; in reality, the entire space would also not be a box), i.e., the set of all the many weights that, once inserted in the AHP formula, lead to the top-selling product having the highest AHP value. The set also contains the true and designated weights of the four clients. In practice, their location in the box is unknown. Two new product variants, V1 and V2, are considered. They constitute what the company is able to manufacture. Let us assume that for client 1, the new variant V1 would truly be the best one, given his/her weights and taking all the variants currently sold into account, while V2 would truly be the best for the two clients with weights between lines C and D. Now, following step 3 of the procedure, it is discovered that V1 is the best variant based on all the sets of weights lying in the region between lines A and B, which happens to capture the weights of client 1. In the case of variant V2, it turns out to be the best product for all the sets of weights located between lines C and D, this finding capturing clients 3 and 4. According to step 4, since the latter subregion of weights is greater than the former, the company makes the decision to start producing variant V2. This decision is correct because V2 is in reality preferred by more clients (two) than V1 (one client), or by a greater subset of the relevant market segment.

But what is the point of this procedure when the true weights are unknown in practice? Because of the larger weight subspace (the case of V2), we can be more confident that there are clients in the relevant market segment for which the variant in question is the best (in the example, the larger subspace managed to capture both the clients). With small subspaces, that confidence is much smaller. Even though the V1 client was captured with the small subspace in the example, we are unaware of that in practice, and there is not much reason to trust such result—if the distribution of the true weights is rather even in the weight space, the small subspaces will at best capture fewer clients than the large subspaces (that’s the case with V1, V2), or they will not capture any client—the V1 client did not have to be captured, so small subspaces are not of much use. We do not know in practice which of the two cases occur, but this is irrelevant because both of them are adverse. When the distribution of the true weights is uneven in the space, additional arguments presented in the second paragraph of the Section 4 apply, their main point being that when a large subspace is very large, as is the case in the example that follows, the character of the weight distribution should not be of much concern, and the large subspace should still be preferred.

The following, more specific example works with three currently sold product variants assessed by three features. The first two features have the property that the higher they are, the better. The third has the opposite property; the lower, the better.

Table 1. Product feature levels of three currently sold product variants.

Characteristic 1	Characteristic 2	Characteristic 3
100	80	70
70	90	66
60	95	66.5

contains the levels of the three characteristics for each product variant.

Normalized feature levels ${\mathit{a}}_{\mathit{i}}^{\ast }=(a_{i1}^{\ast },a_{i2}^{\ast },a_{i3}^{\ast })$ for the ith variant, i = 1, 2, 3, are in

Table 2. Normalized features for the three product variants (rounded to three decimal places).

Characteristic 1	Characteristic 2	Characteristic 3
0.435	0.302	0.320
0.304	0.340	0.341
0.261	0.358	0.338

.

Customers’ individual preferences regarding the three characteristics are unknown, but it is known that the first variant is the one most sold. Using the procedure, the number of vectors $\mathit{w}=(w_1,w_2,w_3)$ whose coordinates sum to one and for which the AHP-based scalar product $\mathit{w}·{\mathit{a}}_1^{\ast }$ is higher than both $\mathit{w}·{\mathit{a}}_2^{\ast }$ and $\mathit{w}·{\mathit{a}}_3^{\ast }$ is 26, when the weight intervals (0, 1) are walked through with step 0.1 for $w_1,w_2$, while $w_3=1-w_1-w_2$, and also $w_1>0,w_2>0$, $w_3>0$. This is a rather rough walk; the step should be smaller in practice to obtain potentially more weight sets (see Section 4 for comments). The 26 weight vectors form a space S1, assumed to be encompassing the unknown weights that underlie the market segment’s true preferences. Now, within steps 2–4 of the procedure, let us envisage product variants whose ith feature lies in an interval with bounds somewhere around the minimum and maximum of the ith column of Table 1. The bounds represent production limits. For each such conceivable variant, let its three generated features be added to Table 1, which will convert the three-row table into a four-row table. The new table can be normalized and evaluated using all the weight sets from step 1, i.e., four variants would be evaluated for each step 1 set of weights. This way, it can be calculated for how many weight sets from step 1, a generated product variant has a higher AHP value than the three existing variants. Specifically, if the new product variants are generated in such a way that for the first characteristic, the interval [85, 99] is walked through with step 1, for the second characteristic, [80, 90] is walked through with step 2, and for the third characteristic, [64, 74] is crossed with step 2, thirteen variants are detected that are better than the existing three variants, with respect to the highest number of step 1 weight sets. That number of weight sets is 25 for each of the 13 variants, which covers almost the entire space of step 1 weights (25/26). The new variants have the potential to appeal to a relevant portion of the market. Specifically, the levels of their features are shown in

Table 3. A space of product designs that may beat a larger part of the current market.

Characteristic 1	Characteristic 2	Characteristic 3
98	90	64
99	82	64
99	84	64
99	84	66
99	86	64
99	86	66
99	88	64
99	88	66
99	88	68
99	90	64
99	90	66
99	90	68
99	90	70

.

The result allows for some flexibility when designing a product, as suggested by Table 3. The entire R code [3] generating the table is shown in Appendix A of the text. The result makes sense, especially with respect to the diversity in the third feature, the flexibility probably given by the fact that the characteristic is not very important, since it is at its worst level in the case of the best-selling variant (the first variant in Table 1).

If there is more than one product configuration in the analytical outcome, as was the case here, it is possible to think about reducing the product set further by finding, using the idea of step 1 of the procedure, the set of weights S2 based on which the currently second most successful product has the highest AHP value. This set would identify the weights of the market segment that preferred the most or the currently second most successful product, the product success still measured by sales. The set of products from Table 3 would then be further reduced in such a way that out of the 13 configurations, those that are the most valuable out of the 13 according to the largest number of weights from S2 would be selected. Such product configurations would have the highest chance of appealing to not only the top-seller segment of the market, defined by the currently most-selling product, but also to the second largest market segment, defined by the currently second most-selling product. It may be worth noting that the weight space for the best-selling product and the weight space for the second best-selling product are disjoint sets.

Theoretically, if the entire “continuous” space of weight vectors was reasonably discretized, the company’s each producible or envisaged product variant could be assessed against the weights from this entire discretized weight space, and not just against those weights that relate to the currently best-selling product, as has been done so far. This effort would try to find a product variant that appeals to as many clients of the entire market as possible, and not just to the clients who bought the currently best-selling product. And this procedure would be justified because whatever weight vector is selected, it determines that one of the currently sold product variants is the best, and so such a weight vector becomes an element of the weight/market segment S1, or S2, or S3, etc. However, taking into account the entire, albeit discretized, weight space may lead to unbearably complex calculations (see Section 4 for further comments). Therefore, the strategy of focusing on the segment of the most successful product, or additionally also on the segment of the second most successful product, is taken here. This procedure should not lead to computational complexity, because if the procedure is focused on the largest segment only, for instance, the number of weights representing it will usually be much smaller for their further processing, compared to the entire (discretized) weight space—in the shown example, only 26 such weights—and obtaining these weights will not be computationally complex either, because there are not usually too many current product variants on the market to hamper the realization of step 1 of the procedure.

Regarding the second information scenario, when customers’ preferences are known, at least within some bounds, it shall be assumed for the sake of the next numerical example that a forum was run and its participants were asked to report their preferences regarding cars. The results of the poll are shown in

Table 4. Clients’ preferences for cars.

Engine	Max. Consumption	Tire Size	Max. Price	Car Type	Transmission
110	9	16	35	S	M
90	8	17	30	S	M
85	8	17	30	H	M
80	7	17	35	SUV	M
90	8	18	35	SUV	M
100	8	18	40	S	A
90	7	18	40	S	M
110	10	20	50	SUV	A
80	7	17	35	S	M
80	8	19	45	H	A

.

The table contains responses from ten clients, regarding desired car feature levels. There are six features a client is interested in: engine power, available in versions 90 kW, 100 kW, 120 kW, and 150 kW, and the clients reported the minimal levels required; fuel consumption, a function of the engine power: 90~7.4 L/100 km, 100~7.9 L/100 km, 120~8.2 L/100 km, and 150~9.2 L/100 km, and the clients reported the highest acceptable consumption; tire size, available in 16, 20, and 22 inches, and the clients reported what size they demanded; car type (sedan, SUV, or hatchback), and the clients reported what car type they demanded; transmission (manual vs. automatic), and the clients reported what transmission they wanted; and price, and the clients reported the highest acceptable prices.

To implement the two-step product-design procedure in the presence of larger amounts of data, a couple tools are required: a programming environment to generate product configurations that can be manufactured and satisfy the needs of at least one client (step 1 of the procedure), and a visualization tool that displays results of the analysis applied to the generated product configurations (step 2 of the procedure). The analytical results show how many clients in the market sample share, within their preferences, various product configurations.

The two-step procedure can be run as follows: product combinations are created in a programming environment for each client. Since a given client reported a minimal engine power required, this condition creates a space for product combinations, while the other independent product features (tire size, car type, transmission type) were reported as fixed, and therefore do not create more space for other combinations of the product features. Once generated, each combination of product features is enriched with the information on the corresponding true fuel consumption and true price, the two dependent features that are of interest to the clients as well. While the combinations of independent features are generated so as to fall within each client’s preferences, this cannot be done with the dependent features, as discussed. The dependent features are determined uniquely by the independent features. Next, the determined true price is compared to the maximal price acceptable to each client and the same is done with the true fuel consumption. These comparisons will usually result in some product combinations being removed from the generated data. The data cleaned this way for each client then contain only the combinations of product features that can be produced and are also in accordance with what the clients demand. This phase can be implemented in any programming environment, and the resulting data may be exported in a proper file format to be processed in the second stage with a visualization tool. The visualization will be done so as to enable the user to select with respect to which product features the frequencies of shared preferences will be counted.

In summary, before step 2, product configurations are generated only with respect to the independent product features, taking into account what can be produced and what clients demand for the product features. This can be done for each client separately. After that, the levels of the dependent features are determined and compared to the clients’ demands regarding the dependent features. This reduces the number of generated configurations. The reduced data then enter step 2 of the procedure.

Table S1, publicly available due to its length at the website referenced below in the Supplementary Materials, shows product configurations based on the preferences from Table 4. Although the true price of a given configuration is not yet attached to the Table S1, it can already be seen that its second row, for instance, will not be part of the reduced table, since the true consumption of 9.2 in the last column of the row is higher than the maximal consumption of 9 acceptable to client 1. The first two rows of the table, related to client 1, are: (Engine, Tire, Max.price, Car type, Transmission, Max. consumption, True consumption) = (120, 16, 35, S, M, 9, 8.2) and (150, 16, 35, S, M, 9, 9.2). Since client 1 demanded an engine of at least 110 kW, two configurations were available for them: the company also produces 120 kW and 150 kW engines when it comes to engine powers of at least 110 kW, hence the two rows for the client.

The designing of an application that analyzes the data in Table S1, avoiding the pitfalls mentioned earlier, and displays the results in a neat form can be found, for instance, in [4,5,6]. Its full description is well beyond the scope of this text, but the steps necessary to achieve the visual results for the car example (Figure 2, Figure 3 and Figure 4) are in Appendix B.

The figures below show the analytical output for the presented car example, and the corresponding application can also be seen in animated action at the website address cited in the Supplementary Materials of the paper. The result, which in this case belongs to the category of bubble graphs equipped with predefined parameters, shows that if the emphasis is placed only on the car type, then three clients, contained in the reduced table, prefer a sedan, another two an SUV, and one client would rather buy a hatchback (Figure 2). Thus, if the company wants to manufacture a single car type, then it should be a sedan. Similarly, Figure 3 shows that if the interest is focused only on the engine power, the most preferred version is that of 90 kW (three clients). The features determining the number of clients with shared preferences are selected via a tool seen on the right-hand side of the figures. Figure 4 shows how many clients prefer different combinations of car type and engine power. Since each combination of these two features is preferred by a single client, it is not clear from this elementary example working only with a handful of clients which combination should be manufactured.

As mentioned earlier, the frequencies may be low, and so the user of the system should be given an option to select with respect to which independent product characteristics the frequencies should be calculated. This is ensured by the parameters on the right. For instance, if the user chooses only the engine power as the feature, the output should display how many clients prefer different engine powers. The engine power is certainly the kind of feature that is determined before the production and cannot be modified after the production. With tire size, the situation is different. Its choice can be made after the production. The focus on a reduced number of product features will allow the application to find more clients who share the same preferences regarding the important features.

It can be summarized for this section that if a company happens to be in the position of having knowledge on clients’ preferences, the clients representing a sample of the entire market, a product configuration out of those that can be produced by the company can be identified which has the potential to address a larger market segment, at least as suggested by the market sample preferences. When the sample is larger, it is necessary to adopt an IT-based approach that will automate many trivial operations that must be performed for the configuration to be detected. These operations involve generating a set of product variants for each client and finding out which of them is shared by as many other clients as possible. When taking these steps, it must be borne in mind that only realizable and client-acceptable product variants make sense for the analysis, which means detecting independent and dependent product features and checking which producible variants fall within the preferences of each client. Only then can the relevant frequencies be counted. The system should also calculate the true number of clients of interest, not counting some of them unwillingly more than once, and allow a selection of product features that will define the depth of the analysis.

4. Discussion

It is important to note for the case of little market information that the exposition of the methodology and the subsequent example worked with the assumption that product characteristics were independent. This will often not be true, as price is usually one of the observed features, as well, and price is a function of other product characteristics. In such cases, the procedure follows the same steps except that the values of product variants are not calculated by the AHP expression $A^{\ast }\mathit{w}$, where $\mathit{w}$ are the weights of the product characteristics and $A^{\ast }$ is the matrix of normalized levels calculated for each variant and each characteristic, but by applying the Analytic Network Process (ANP) $A^{\ast }{(\mathit{I}-\mathit{V})}^{-1}\mathit{w}$ formula, where $\mathit{I}$ is the identity matrix and $\mathit{V}$ is the matrix of normalized evaluations of relations among the product characteristics [7]. In the case of independent characteristics, $\mathit{V}=\mathit{o}$ and the ANP formula becomes the AHP formula.

Secondly, even if the AHP worked as a model without flaws, there would still be situations when the little-information procedure could fail. These situations are related to a potentially uneven density in the distribution of the true sets of weights in the step 1 space. For instance, it could happen in the given example that a majority of the clients from the analyzed segment, who truly preferred V1, had their true weights located in the narrow region between lines A and B, while there were just a very few clients, preferring V2, with their true weights scattered sparsely in the region between lines C and D. Then, the result of the example above, recommending V2, would lead to a bad decision, the version V2 being preferred by a pronounced minority of the clients. In this case, even though the subregion pointed to V2, as large as this subregion was, it contained weights of only a handful of clients due to the sparsity in the spatial deployment of the weights. The density of the weights cannot be, of course, even remotely estimated without further information about the market, and hence such a pathological effect cannot be prevented by the method under the imposed information constraints. The method needs to follow the statistical principle of uncertainty to work properly—if the distribution of the true weights is unknown, assume, at least to a great extent, that the distribution is rather even in the weight space, without occurrences of patches with high density of weights. Nevertheless, if the set M of a winning product design is very large, covering a vast majority of the weight space, as was seen in the example (25 out of 26), the pathological effect is unlikely to occur. Also, if the new product features are good enough, it can be expected that such a product will be often best by a large enough subspace of weights.

If feature preferences are available from a sample of clients, their empirical distributions can be drawn to see if the pathological effect can occur. Since each weight set is a point in the multidimensional space, and the objective of the visual check is to see if there are many weight points close to each other, several graphs can be drawn for the sample, each depicting the distribution of a selected point coordinate. If the graphs suggest irregularities in the distribution of the points, this may signal a potential problem. Several graphs are needed, since if the weight dimension is higher, the points cannot be obviously displayed in a single graph. For the case of two-dimensional weight space, for instance, Figure 5 shows partly concentrated points in the lower part of the plane.

Further, it is worth noting that the procedure can potentially yield quite a few product designs that may appeal to the market (their M sets will have the same size), which would be a positive quality of the result. The company would at least have enough options to choose from. If, on the contrary, the method returns too few product designs, even just one, the company can always expand this list by taking into account not only the product configurations whose set M is the largest, but also the configurations whose set M is the second, or even third largest. These sets can still be big. The method can thus always be used in accordance with companies’ needs regarding the diversity of the analytical result.

Last but not least, reflecting on the procedure suggested for the case of little information, one might think that maybe a similar procedure could be formulated, in the form of a more elegant optimization problem, should the objective be to find one “winning” product design which minimizes production costs, and for which there is at least one set of weights for which the design beats the market. This is possible, the formulation being to minimize, with respect to $a_{new,1},\dots ,a_{new,k}$, a production cost function:

$$Costs(a_{new,1},\dots ,a_{new,k}) \text{subject to}$$

(1)

$$a_{new,j}\in I_j,j=1,\dots ,k,$$

(2)

$$w_j\in \left[0,1\right],j=1,\dots ,k,$$

(3)

$$w_1+\dots +w_k=1,$$

(4)

$${\ddot{a}}_{new,1}{w}_1+\dots +{\ddot{a}}_{new,k}{w}_k\ge {\ddot{a}}_{i1}{w}_1+\dots +{\ddot{a}}_{ik}{w}_k,i=1,\dots ,n,$$

(5)

$${\ddot{a}}_{11}{w}_1+\dots +{\ddot{a}}_{1k}{w}_k\ge {\ddot{a}}_{i1}{w}_1+\dots +{\ddot{a}}_{ik}{w}_k,i=2,\dots ,n$$

(6)

Here, $a_{new,j}$ is the level of the jth feature of the new, sought product, ${\ddot{a}}_{new,j}$ is its normalized level, $w_j$ is the weight of the jth product feature, and ${\ddot{a}}_{ij}$ is the normalized level of the jth feature of the ith currently sold product, i = 1 denoting the best-seller. Expression (1) is viewed as a function of variables $a_{new,1},\dots ,a_{new,k}$, $w_1,\dots ,w_k$ depending mathemaically only on $a_{new,1},\dots ,a_{new,k}$ ($f(x,y)=x$ is another example of this situation, a function of two variables depending only on $x$). The problem seeks both $a_{new,1},\dots ,a_{new,k}$ and $w_1,\dots ,w_k$. In other words, according to conditions (3) and (4), the problem seeks weights, for which, according to (6), the best-selling product is indeed the top seller by AHP (this is step 1 of the procedure described earlier), and within all such acceptable weights, new and potentially better products are sought (condition (5)), taking into account only what the company can technically produce (condition (2)). Out of all such best new products, the one that is cheapest to produce is selected by (1). The minimization replaces the earlier objective to choose out of the products that satisfy conditions (2)–(6) the one(s) that appear to be most appealing to the market, the appeal being measured by the number of weights for which they seem to be the best product (even better than the current top seller). However, there would be several severe problems with this approach: (1) the procedure does not reflect in any way the number of weights for which the optimal product is the best one and so it may appeal to too few customers (potentially to only one) despite minimizing the company’s costs; (2) the problem will generally be difficult to solve because it assumes by (2) that an infinite number of product combinations can be produced (unlikely in practice, requiring another condition “$a_{new,j}$ is integer”, for instance, to discretize the problem), and because the objective function (1) will probably be a nonlinear function. Nonlinearity is also hidden in conditions (5) and (6) because of the normalization. Hence, practically speaking, the problem would fall in the category of a nonlinear and mixed-integer mathematical problem, a potentially very difficult problem to solve [8,9]. Therefore, the procedure described earlier, although not being as elegant as problem (1)–(6) due to the discretization and need to look for different interesting weights through programmed cycles and conditions, makes more sense for practical purposes.

It should be noted that AHP is not the only model that can be applied to describe the decision-making process of the market. Other techniques, perhaps most frequently referenced in literature, include methods of the AGREPREF, ELECTRE, or PROMETHEE type, which are based on sensitivity thresholds [10]. None of the techniques is regarded as the very best, regardless of the problem at hand [11]. Each of the methods has some advantages and disadvantages [12]. Each of them is based on a different principle. This means, unless one has a specific decision problem in mind, that, generally speaking, more techniques can be used to put the ideas presented in this text into practice. The selected technique should not be too complex for companies, however, which is one of the reasons AHP was exploited. Another criterion that determined the method selected was whether the procedure is able to rank variants from best to worst, or whether it can only separate better variants from worse. Taking this factor and the factor of simplicity into consideration, AHP should be preferred to the methods based on sensitivity thresholds because application of the latter is complicated by looking for not only the weights of the decision-making criteria, but also for the sensitivity thresholds, and with PROMETHEE-type methods also for preferential functions. Additionally, in the case of AGREPREF and ELECTRE methods, in their basic form, complete ranking of variants is not guaranteed, and the resulting ranking relation is not even transitive. Another very popular approach in the decision-making modelling is represented by the TOPSIS method. TOPSIS could be potentially used instead of AHP in the presented procedure, i.e., it could be applied to find the various conceivable weights (step 1 of the suggested procedure), and then, based on the weights found, to detect the best product. Despite that, AHP may have several advantages over TOPSIS. TOPSIS, in its original form, does not work with the possibility that decision criteria can be intertwined, as opposed to AHP in its extended network-based form. Some attempts to extend TOPSIS in this sense were already done [13], but the extension is not always applicable (there has to be more variants than criteria when the procedures described in [13] are to be applied). Overall, however, the experience from practice is such that with the same set of weights, the two methods yield more often than not the same rankings of the variants, and so no harm will be done if any of the two methods is used in practice to implement the four steps of the suggested procedure.

Generally, an optimal product or an entire product line has been historically sought either by multidimensional scaling methods, which assume that the utility of a product is given by how far it is from an ideal point in the space of product variants, a methodology postulating that product utilities are symmetric around the ideal product point, or by conjoint analysis-based methods which have no specific assumption about the form of utility functions. The approaches work with different data sources. The latter methods derive product utilities either directly from the quantitative nature of product characteristics, or via interviewing a sample of customers (especially when the product design contains qualitative features). The AHP-based approach is not distance-based, and it takes into account the levels of product attributes together with their importances. Thus, for comparative reasons, the method presented here is closer to the conjoint analysis-based methods.

The suggested procedure focuses primarily on finding a product that will appeal to many customers. Hence, it has primarily the market share in focus. The conjoint-based methods solve the problem of maximizing the producer’s profit (“the seller’s welfare problem”), sometimes while maximizing at the same time the well-being of the buyers (“the buyer’s welfare problem”), using observed, or estimated, utilities of individual levels of the product features (overall product welfares are then sums of the individual-feature utilities subject to some constraints). These optimization problems can theoretically be solved either by way of complete enumeration, calculating welfares of all within-production-limits conceivable product variants, or by sophisticated algorithms which look for a path to move closer to the optimal solution without the need to evaluate each product variant. The problem is that given a number of product features together with their different levels and different product portfolios, the total number of combinations to be evaluated increases exponentially even to hundreds of billions of combinations. This makes complete enumerations from the practical point of view difficult, or even impossible. The methods that try to avoid these problems are based on heuristics. Since the method proposed in this text centers on the market share, while the heuristic method focus on the producer’s profit, their direct comparison is elusive, although the heuristic methods do not generally attain the optimal profit, rather a high profit, while for the proposed method, the following can be said: the procedure takes as the “winning product design” the design that is best by a large number of weights from the weight space; if we assume that this means that such a product variant will have a larger market share, it could also rank among the more profitable variants provided its profit margin is the same or higher than that of any other product variant. What if there is another product variant on the side of the producer, not considered by the method as the best one, because it is not the best by the largest number of weights from the weights space, whose profit margin would be higher than that of the winning product variant, if it was produced, and in total, it would bring a higher profit? Theoretically, this can happen. On the other hand: (1) the winning variant, satisfying many customers, can be expected to have at least some of its attributes to be rather boosted (see the example), hence it will not be the cheapest to produce and so, setting a fixed profit margin, its price and the profit, as a percentage of the costs, will be rather higher than lower; (2) there will usually be more winning product variants with the same estimated market share (see the example), thus the producer can choose out of them the most profitable variant, bringing itself to or closer to the most profitable variant overall; and (3) it is difficult to justify the argumentation that there might be a variant with lower market share that could bring a higher total profit, especially if the resulting winning product variant is best according to an overwhelming number of weights (see the example) because, unless it is a market of high-end luxurious products, products that sell less (at least as estimated by the AHP model) can be expected to have less boosted features, thus cheaper production and smaller profit for a fixed profit margin, and additionally they will probably sell in smaller numbers than the product defined as the winning by the method. Thus, even though it is impossible to guarantee that the winning product is the most profitable one, it should bring the producer high profits rather than lower profits. Hence, in some sense, the heuristic methods and the method proposed here can be to an extent similarly oriented: to achieve higher profits. This argumentation makes them now a bit more comparable.

To make the comparison of the proposed method with the heuristic methods, a description of the latter follows first, then the comparison is made. There are several classes into which the heuristic methods can be divided.

The first class contains procedures that move within the space or product features. Article [14], a representative of the class, proposed a method that selects product(s) randomly, then through a random selection of a feature and a random change of its value tests if it leads to a more profitable product portfolio. This procedure continues until it cannot find a more profitable portfolio. The method is not guaranteed to find a global optimum. Ref. [15] is an example of employing genetic algorithms, and is also an important member of the class. The method starts with a population of random solutions, instead of one solution. The fittest individuals/products then mate by changing its features, with a flavor of mutation, to create a new and better “population”. This continues until a stopping condition is achieved. The method is not guaranteed to find a global optimum, actually not even a local optimum, but it often attains a local optimum.

The second class contains methods that change entire products, not just some of their features. The class includes the strategy of greedy heuristics. This strategy was introduced in [16] and extended in [17]. The algorithm starts with a single product that maximizes profits and in the subsequent steps, it always adds one other product to the already selected product line which maximally increases the portfolio-based profit. The procedure is not guaranteed to find even a local optimum. A similar algorithm is represented by the “interchange heuristic”: it randomly selects a product portfolio and then tests, in each step, whether any of the current portfolio products can be swapped with a non-portfolio product so that the portfolio-implied profit is increased. The method looks for an interchange that maximally increases the profit. When it cannot find a beneficial swap, it stops. The procedure is not guaranteed to find a global optimum, just a local optimum. The third class involves methods that work only with a subset of all product features and evaluate product variants only on these subsets first. This allows them to eliminate in advance some adverse feature combinations before considering other features. Methods of this type include the dynamic programming method presented by [18] and their extension to an entire product portfolio, as presented in [19]. The methods are not guaranteed to find local optima.

None of the major algorithms that have been presented find global optima, some of them not even local optima. They may find them, but the methods will not recognize it. Some of the methods work with a single optimal product, others with a whole product portfolio. Recent development has moved from the heuristics to procedures that would finally be able to find global optima. Such a method has indeed originated, but it is too complex for companies to apply them (to outline the complexity, the calculations last more than one day). The procedure combines the so-called Lagrangian relaxation strategy [20] and a branch-and-bound method [21].

Compared to the above, the proposed method has some advantages and disadvantages, although direct comparison is also complicated by the fact that while the proposed method is more focused on detection of market preferences, disregarding the possibility that the problem can be very complex with respect to the accompanying calculations, the heuristic methods deal, on the contrary, primarily with the calculation problems, not with the identification of market feelings about the product features.

One of the advantages of the method is, as has just been outlined, that, through approximate identification of weights of the entire market, it tries to communicate with the perceptions of the entire market. This is not a feature of the methods mentioned earlier, which take utilities of the individual levels of product features as given, obtained, and then focus on the mathematical mechanics of finding an optimal product(s) selection. The methods take into account a sample of customers at best, when detecting the utilities of product features, as opposed to the AHP-based approach presented here which, through the weight space, works with many possible views on how beneficial each product feature might be, the amount of benefit being described by the weighed form of each product feature level before these weighed values are added together to get the aggregated value of a product variant. This connection with the market, although in the form of a model—the AHP model—takes place without the need to interview anybody, though this is true only when the analyzed product is described by quantitative features. This also shows a disadvantage of the method: when a qualitative feature is present, it cannot be used. Another advantage of the presented method is that it is simpler than the heuristic methods mentioned; however, this is only true when the complexity of the problem is not too large, otherwise the proposed method will run into the same complexity problem the heuristic methods originated for. The problem of a reasonable extent can be reduced, however. To give an example, let the analyzed product have six features (not a small number for just quantitative features), each with six levels. The weight space is theoretically continuous, not discrete as shown in the example, but overly subtle divisions of the intervals [0, 1] to approximate the weight space continuity when building the weight space are unnecessary, since a small change in the setup of the weights is unlikely to change the ranking of the existing variants (the first step of the procedure). Hence, a division by, say, 0.05 should suffice for practical purposes; if a product variant turns out to be best for a given weight vector, it can be expected to be the best for a sufficiently close “true” weight vector, as well. The division gives 20 possible weight values in each interval and the example currently works with six weights. This suggests that when looking for the proper design through a full enumeration, trying to satisfy the entire market, not just the best-product segment, $6\times 6\times {20}^6$ evaluations would have to be done, which is obviously a huge number (roughly three trillion). However, the weights sum to one, so the sixth weight in this case is given by the remaining five which must some to one at most. This reduces the original number of weight combinations at ${20}^6$ significantly, and even more so given that the remaining five freely moving weights must some to one, so many of their combinations, which exceed one in sum, can be left out. Also, and even more importantly, the company does not have to observe all 36 product variants when evaluating them with a given weight vector; when the company encounters a product variant that is not best for the given weight vector, it may immediately skip all the remaining product variants with at least one worse feature, since any such variant will not pass the test given the form of the AHP weighted sum. This can quite reduce the number of operations further. Additionally, as has been mentioned, another huge reduction results from focusing the method on the best-product segment, or two best product segments (the weight subspaces S1 and S2), not the entire market.

Nevertheless, for very large problems, which can be devised for any method including the proposed one, where the described reductions will not be sufficient, the presented methodology should rather be taken as a procedure that is more focused on how to formulate the problem of finding an apt product than how to mathematically solve it in a reasonable time. The problem will most likely be complex, for instance, when not just one product is searched, but an entire portfolio of m products is desired, since this will add to all the combinations the multiplication by the combinatorial number (m number of product variants). Hence, the proposed method may be more suitable for companies that desire to produce a single product variant, such as start-up companies at the beginning of their existence.

To sum up, the suggested procedure has the following advantages and disadvantages:

Advantages: It detects market segments, so it takes into account the broader market preferences, which additionally allows to detect individual market segments and focus only on the relevant ones, bringing down the complexity of the calculations; the algorithm is also mathematically simple.

Disadvantages: The method needs quantitative features; it is better suited for finding a single convenient product variant, not an entire product portfolio, as far as the complexity of the calculations is concerned; if the weight space found in step 1 of the procedure is not large enough, the method will be less trustworthy.

5. Conclusions

The paper suggested two procedures that can be implemented when a new product design is searched. The character of the procedures depends on how much information is known about the market. If a market sample of clients is available together with the clients’ preferences related to relevant product features, a set of product configurations can be generated, each configuration being in line with the preferences of at least one client, and subsequently the configuration that is shared by the largest number of clients can be selected. While this idea is straightforward, some issues can be encountered when the procedure is implemented automatically by a computer system due to a large number of clients. The paper focused mainly on these problems and described a build-up of a computer system that avoids these pitfalls. When, on the contrary, there is little information about the market, it is possible to use a mathematical model that at least approximates the market’s decision-making, and then identify product designs that might be preferred by the market, given the estimated decision process. This second approach relies on the theory of Analytic Hierarchy Process (AHP), which has the potential to estimate, with reasonable precision, the decision-making process of individuals. Once the decision-making is approximated, the second procedure searches for product design(s) that appear to be the best according to this decision process, the basic idea relying on the fact that the success of currently best-selling products is necessarily the result of a market decision. Both approaches were also illustrated with numerical examples, the implementation of which is further detailed in the appendices below.